Find the intersection of the sets
`A={1,2,3,4,5,6}`, `B={2,4,5}`, `C={2,6}` and show that `(AnnB)nnC=Ann(BnnC)`.

Answer

To solve the problem, we need to find the intersection of the sets \( A \), \( B \), and \( C \), and then show that \( (A \cap B) \cap C = A \cap (B \cap C) \).

### Step-by-Step Solution:

1. **Identify the Sets:**
- \( A = \{1, 2, 3, 4, 5, 6\} \)
- \( B = \{2, 4, 5\} \)
- \( C = \{2, 6\} \)

2. **Find \( A \cap B \):**
- The intersection \( A \cap B \) consists of elements that are in both \( A \) and \( B \).
- Common elements: \( 2, 4, 5 \)
- Thus, \( A \cap B = \{2, 4, 5\} \)

3. **Find \( A \cap C \):**
- The intersection \( A \cap C \) consists of elements that are in both \( A \) and \( C \).
- Common elements: \( 2 \)
- Thus, \( A \cap C = \{2\} \)

4. **Find \( B \cap C \):**
- The intersection \( B \cap C \) consists of elements that are in both \( B \) and \( C \).
- Common elements: \( 2 \)
- Thus, \( B \cap C = \{2\} \)

5. **Calculate \( (A \cap B) \cap C \):**
- We already found \( A \cap B = \{2, 4, 5\} \).
- Now we find the intersection of this set with \( C \):
- \( (A \cap B) \cap C = \{2, 4, 5\} \cap \{2, 6\} \)
- Common element: \( 2 \)
- Thus, \( (A \cap B) \cap C = \{2\} \)

6. **Calculate \( A \cap (B \cap C) \):**
- We already found \( B \cap C = \{2\} \).
- Now we find the intersection of \( A \) with this set:
- \( A \cap (B \cap C) = A \cap \{2\} \)
- Common element: \( 2 \)
- Thus, \( A \cap (B \cap C) = \{2\} \)

7. **Conclusion:**
- We have found that \( (A \cap B) \cap C = \{2\} \) and \( A \cap (B \cap C) = \{2\} \).
- Therefore, \( (A \cap B) \cap C = A \cap (B \cap C) \).

### Final Result:
\[ (A \cap B) \cap C = A \cap (B \cap C) = \{2\} \]